Editing Generating function (section)

====Examples====

The functions {{math|''e''<sup>''z''</sup>}}, {{math|log ''z''}}, {{math|cos ''z''}}, {{math|arcsin ''z''}}, <math>\sqrt{1 + z}</math>, the [[dilogarithm]] function {{math|Li<sub>2</sub>(''z'')}}, the [[generalized hypergeometric function]]s {{math|''<sub>p</sub>F<sub>q</sub>''(...; ...; ''z'')}} and the functions defined by the power series
<math display="block">\sum_{n = 0}^\infty \frac{z^n}{(n!)^2}</math>

and the non-convergent
<math display="block">
\sum_{n = 0}^\infty n! \cdot z^n
</math>
are all holonomic.

Examples of {{mvar|P}}-recursive sequences with holonomic generating functions include {{math|''f''<sub>''n''</sub> ≔ {{sfrac|1|''n'' + 1}} {{pars|s=150%|{{su|p=2''n''|b=''n''|a=c}}}}}} and {{math|''f''<sub>''n''</sub> ≔ {{sfrac|2<sup>''n''</sup>|''n''<sup>2</sup> + 1}}}}, where sequences such as <math>\sqrt{n}</math> and {{math|log ''n''}} are ''not'' {{mvar|P}}-recursive due to the nature of singularities in their corresponding generating functions. Similarly, functions with infinitely many singularities such as {{math|tan ''z''}}, {{math|sec ''z''}}, and [[Gamma function|{{math|Γ(''z'')}}]] are ''not'' holonomic functions.